A player i in a simple game (N; v) is called a veto player if v(S) = 0 for every coalition S that does not contain i. The player is called a dictator if v(S) = 1 if and only if i ∈ S.
(a) Prove that in a simple game satisfying the property that v(S) + v(N \ S) = 1 for every coalition S ⊆ N, there exists at most one veto player, and that player is a dictator.
(b) Find a simple three-player game satisfying v(S) + v(N \ S) = 1 for every\ coalition S ⊆ N that has no veto player.